Large Deviations and the Generalized Processor Sharing Scheduling: Upper and Lower Bounds Part II: Multiple-Queue Systems

We prove asymptotic upper and lower bounds on the asymptotic decay rate of per-session queue length tail distributions for a single constant service rate server queue shared by multiple sessions with the generalized processor sharing (GPS) scheduling discipline. The special case of a two-queue GPS system has been dealt with separately in Part I of the paper [33], where exact bounds are obtained for each queue. A general multiple-queue GPS system is treated in this part (Part II) of the paper and tight upper and lower bound results are proved by examining the dynamics of bandwidth sharing nature of the GPS scheduling. We are not able to obtain exact bounds in this general case due to the complex nature of dynamic bandwidth sharing under the GPS scheduling. The proofs use sample-path large deviation principle and are based on some recent large deviation results for a single queue with a constant service rate server. These results have implications in call admission control for high-speed communication networks.